It's totally safe to visit Athens. Many people from other countries are geocaching all these days, and there has been not a single comment in their logs about lack of safety, you can check for yourself too.
Feel free to contact any of us here for any other questions you may have (yes, that includes extra hints too).
I reckon you are Dutch, there is a Dutch couple that's been geocaching in Athens for two weeks, hildesd and Cake1618, you can ask them directly too.
And when you are in Athens give us a note, who knows maybe you can meet some of us.
Have a perfect time in Greece.